is there a way to make blender look for textures in the current directory?
You can store paths relative.

Save your file first. When importing an image, make sure the checkbox Relative Path is checked. (Lower left of the open image dialog.)



Examining the image in the image editor will reveal, that it's path starts with two slahes  //.


  When relative paths are supported, the File Browser provides a Relative Path checkbox, when entering the path into a text field, use a double slash prefix (//) to make it so.





  Relative paths are the default but this can be changed in the File tab of the User Preferences Editor.


So make sure, that relative paths are used by default by checking the box.



Now all paths relativ. Moving the .blend file and all image (etc) files, preserving their relativ location in the file structure, will not break the link in the .blend file.

However, if the relativ path changed (e.g. you renamed the images folder to textures), the links will be broken. You can restore them by searching for missing files. Go to File > External Data > Find Missing Files. Choose the directory containing the missing files and Blender will try to reconnect them.



Also next to this menu entry is the useful "Make all paths relative".